The ASG approach to quantum algorithms provides intriguing links between quantum computation and many different areas: the analysis of spectral gaps and groundstates of Hamiltonians in physics, rapidly mixing Markov chains, statistical zero knowledge, and quantum random walks.Expand

A lower bound on the possible speed up by quantum walks for general graphs is given, showing that quantum walks can be at most polynomially faster than their classical counterparts.Expand

This paper shows how to perform fault tolerant quantum computation when the error probability, q, is smaller than some constant threshold, q.. the cost is polylogarithmic in time and space, and no measurements are used during the quantum computation.Expand

A solution for the subroutine problem: the general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations.Expand

The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.Expand

This paper provides a self-contained and complete proof of universal fault-tolerant quantum computation in the presence of local noise, and shows that local noise is in principle not an obstacle for scalable quantum computation.Expand

Any language in BQP has a QPIP, and moreover, a fault tolerant one, and two proofs are provided: the simpler one uses a new (possibly of independent interest) quantum authentication scheme (QAS) based on random Clifford elements, which is not fault tolerant.Expand

An explicit and simplePolynomial quantum algorithm to approximate the Jones polynomial of an n strands braid with m crossings at any primitive root of unity e2πi/k, where the running time of the algorithm is polynometric in m, n and k.Expand

The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Some illegal configurations cannot be ruled out by local checks, and are instead ruled out because they would, in the future, evolve into a state which can be seen locally to be illegal.Expand

We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of &nradic; lie in NP intersect coNP. The result (almost) subsumes the three… Expand